I know that hFE is not a particularly informative or reliable piece of BJT data and consequently the best designers create designs which function well without much regard to it but...
Out of interest, at what point along the active region should it be measured? Exactly mid-way between cut-off and saturation? Is there a recognized standard?
The hfe is measured at any bias point or multiple bias points the manufacturer has determined useful for anyone using the transistor.
Fot e.g. Fairchild BD137, you have the hfe at VCE = 2V and three Ic values 5mA, 500mA and 150mA. For Fairchild BC547 you just get one value at Vce = 5V and Ic = 2mA. Both transistors just indicate either a huge range of hfe min/max values, or just minimum.
The thing is, for any useful circuit, you simply need the hfe to be large enough to work, and since the range is huge, the circuit must not depend on any specific hfe value. If the circuit just requires some minimun hfe then it will work as long as the transistor is specified to have at least that hfe.
Typically you want it specified (min/max values) at some useful current for the intended range of applications.
For transistors intended for use as a switch, it's mostly just important that hFE is high enough for the base drive.
For analog applications the designer may choose to use circuits that are more sensitive to hFE so transistors designed and specified for that kind of circuit tend to have hFE ranges specified at reasonable currents for (say) an amplifier. For example, the once-ubiquitous Toshiba 2SC1815 has 4 'beta bins' with 'Y' being the most popular. These are generally not randomly determined, you order C1815Y you gete parts that have hFE between 120 and 240 at 2mA Ic and Vce = 6V.
As you can see, the typical characteristics can be further predicted from those values:
For use as a switch (eg. a relay driver or whatever) the minimum hFE at Ic = 150mA and Vce(sat) at Ic = 100mA will generally suffice.
